Can an employer lower your wages after getting transferred from CA to Texas

Some employers have what are commonly called "cost of living" provisions used in the calculations of wages. That means if an employee transfers from an area with a high cost of living to an area where the cost of living is lower ---- then even doing the same job, the wages are lowered. A good example of this is the airline industry, in many of the union contracts. You should find out from your HR department if a transfer will effect your wages before you put in for that transfer.